| 摘要: | 我們通常都會使用傳統的常態近似方法計算信賴區間，但是當處理包含大量零值類型的資料時，常態近似法結果會變得相當不準確。 Kvanli、Shen和Deng（1998）提出最大概度比法來處理這種資料，所建立出來的信賴區間比傳統常態近似方法更加準確。本文利
用 Chen和Sitter（1999）將概度函數加權所發展出的擬概度函數方法來分析含有大量零值的資料，依輔助訊息大小排序後分群，使用 Cochran（1977）提出的不同機率抽取樣本的模式，再以不同權數和相同權數建立信賴區間。並探討在各種相關係數ρ與非零值比例α下，信賴區間上下界的平均值和涵蓋率的表現。
In survey sampling, traditional normal approximation is commonly used to construct confidence intervals of the finite population mean. However, when the finite population contains a large proportion of zeroes, the normal approximation may have very poor coverage rate even when the sample size is large. Kvanli, Shen and Deng (1998) propose a parametric likelihood approach to construct a confidence interval and demonstrate that the likelihood ratio based confidence interval has more precise coverage rate. Chen and Sitter (2002) propose a pseudo likelihood function to overcome the difficulties of lacking of exact likelihood. The approach can be used in the present problem. We first sort the corresponding auxiliary information from the smallest to the largest and divide them equally into several groups, then draw a sample according to an unequal probability sampling design (see Cochran 1977). We develop pseudo likelihood ratio intervals using two different weights and discuss their performance with respect to correlation coefficient ρ and nonzero proportion α, and also analyze their lower and upper average bounds and coverage rates. |